Geometric Differences between the Burgers and the Camassa-Holm Equations
Résumé
The Burgers equation and the Camassa-Holm equations can both be recast as the Euler equation for a right-invariant metric on the diffeomorphism group of the circle, the L2-metric for Burgers and the H1-metric for Camassa-Holm. Their geometric behaviors are however very different. We present a survey of this geometrical approach and discuss these differences.